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arXiv · 1407.2966

Bounded Negativity and Arrangements of Lines

Thomas Bauer·Sandra Di Rocco·Brian Harbourne·Jack Huizenga·Anders Lundman·Piotr Pokora·Tomasz Szemberg
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Abstract

The Bounded Negativity Conjecture predicts that for any smooth complex surface $X$ there exists a lower bound for the selfintersection of reduced divisors on $X$. This conjecture is open. It is also not known if the existence of such a lower bound is invariant in the birational equivalence class of $X$. In the present note we introduce certain constants $H(X)$ which measure in effect the variance of the lower bounds in the birational equivalence class of $X$. We focus on rational surfaces and relate the value of $H({\mathbb P}^2)$ to certain line arrangements. Our main result is Theorem 3.3 and the main open challenge is Problem 3.10.

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Thomas Bauer, Sandra Di Rocco, Brian Harbourne, Jack Huizenga, Anders Lundman, Piotr Pokora, Tomasz Szemberg. 2014-11-05. Bounded Negativity and Arrangements of Lines. https://doi.org/10.1093/imrn%2Frnu236

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